CN115201759B - Radar embedded communication waveform design method based on singular value decomposition - Google Patents
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Abstract
The invention relates to the field of radar embedded communication, in particular to a radar embedded communication waveform design method based on singular value decomposition, which comprises the following steps: s1, after a radar irradiates an REC working area, an RF tag oversamples radar signals; s2, circularly shifting an oversampled radar signal to construct a Toeplitz matrix; s3, singular value decomposition is carried out on the Toeplitz matrix, and characteristics of radar signals are analyzed; s4, dividing the radar signal into a main space component and a non-main space component according to the singular value size; s5, constructing a waveform generation matrix based on singular value decomposition; s6, randomly generating K waveform construction keys; and S7, multiplying the waveform generation matrix with the K waveform construction keys to generate K REC waveforms. The similarity of the REC waveform and the radar echo constructed by the invention can be quantized, the freedom degree of waveform design is doubled on the premise of not reducing the communication reliability and anti-interception performance of the REC waveform, and meanwhile, the complexity of a waveform design algorithm is greatly reduced.
Description
Technical Field
The invention relates to the field of radar embedded communication, in particular to a radar embedded communication waveform design method based on singular value decomposition, which is a radar embedded communication waveform design method with low computational complexity and high design freedom.
Background
With the rapid development of communication technology and radar technology, the electromagnetic spectrum becomes more crowded, the spectrum resources are increasingly stressed, the interference phenomenon among different users is more remarkable, and people are forced to start to research new technologies capable of enabling the radar and the communication to share the spectrum. From another point of view, conventional wireless communication is very easily detected and intercepted due to natural openness and broadcasting, and development of a wireless communication system with high security and reliability is not slow. The professor bronst in 2007 proposed a novel low-probability of interception (Low Probability of Intercept, LPI) communication scheme (Blunt S D, yantham p.wave form design for Radar-embedded communications [ C ]// International Waveform Diversity and Design Conference, 2007:214-218.) that generates a low-power communication waveform with concealment characteristics by remodulating a high-power Radar echo, and then embeds the communication waveform into the Radar echo for concealment transmission, i.e., radar embedded communication (Radar-Embedded Communication, REC). The REC technology can not only realize spectrum sharing of communication and radar, but also ensure concealment of the information transmission process.
The working principle of REC is shown in fig. 1, the cooperative or non-cooperative radar irradiates the whole area, and a Radio Frequency (RF) tag carried by a target of the friend can perform signal sensing, feature extraction and waveform reconstruction on a radar signal to generate a communication waveform with hidden characteristics, and the communication waveform is synchronously transmitted along with radar scattering echo. The cooperative receiver demodulates and recovers the received signal, extracts hidden information in the received signal, and completes hidden communication. The whole process can also have an interception receiver for uninterrupted detection of the communication signal.
The communication waveform design is the primary content of the REC technology, and the existing REC communication waveform design method mainly comprises four types: the non-primary spatial feature vector serves as a communication waveform (EAW), a non-primary spatial feature vector Weighting (WC), a primary spatial processing (Dominant Projection, DP) (Blunt S D, yantham p.waveform design for radar-embedded communications [ C ]// International Waveform Diversity and Design Conference,2007:214-218 ]), and a shaping primary spatial processing (Shaped Dominant Projection, SDP) (metacalf J G, saiin C, blunt S D, et al.analysis of symbol-design strategies for intrapulse radar-embedded communications [ J ]. IEEE Transactions on Aerospace and Electronic Systems,2015,51 (4): 2914-2931 ]), wherein the communication waveform generated by the DP algorithm and the SDP algorithm has better communication reliability and LPI performance.
Since the concept of REC was proposed, waveform design has been a key technology for REC. For example, the orthogonal waveform design method of radar embedded communication (national invention patent: an orthogonal waveform design method of radar embedded communication (ZL 201910243545.8)) can lead the generated REC waveforms to be completely orthogonal, and the radar embedded communication waveform design method of extraction water injection molding can reduce the complexity of waveform design (national invention patent: an radar embedded communication waveform design method of extraction water injection molding (ZL 2021115034157)). However, the existing REC waveform design methods are all to convert the toeplitz matrix constructed by the radar signal into a square matrix capable of decomposing the eigenvalues, and then design the REC waveform based on the eigenvalue decomposition method, and are not directly studied for the radar signal. This brings about the following problems: 1. because the conventional REC waveform design algorithm transforms the toeplitz matrix constructed by the radar sampling sequence, the similarity between the designed REC communication waveform and the radar echo cannot be quantized, and the concealment of the REC waveform cannot be estimated; 2. the degree of freedom of the traditional REC waveform design algorithm is not high enough, and the waveform set is difficult to replace periodically so as to reduce the intercepted risk; 3. the traditional REC waveform design algorithm has higher calculation complexity, can increase the response delay of the radio frequency tag, and affects the time precision of the embedded communication signal. Aiming at the problems, the REC waveform design scheme based on singular value decomposition (singular value decomposition, SVD) is provided, the similarity between radar echo and REC communication waveforms can be well quantified, the waveform design freedom is doubled on the premise of not reducing the communication reliability and anti-interception performance of the REC waveforms, and meanwhile, the complexity of a waveform design algorithm is greatly reduced.
Disclosure of Invention
Aiming at the problems, the invention provides a radar embedded communication waveform design method based on singular value decomposition (singular value decomposition, SVD). Compared with the traditional REC waveform design method, the method can well quantify the similarity between the radar echo and the REC communication waveform, improves the waveform design freedom by one time on the premise of not reducing the communication reliability and the anti-interception performance of the REC waveform, and greatly reduces the complexity of a waveform design algorithm.
The invention adopts the technical scheme that: a design method of radar embedded communication waveform based on singular value decomposition comprises the following steps:
after the S1 REC working area is irradiated by the radar, the radio frequency tag oversamples radar signals, and a radar signal vector r with a sampling length of NM is expressed as:
r＝[s 1 ,s 2 ,s 3 ,…,s NM ] H , (1)
where r is the sampled radar signal vector, s 1 ,s 2 ,s 3 ,…,s NM Oversampling data for radar signals, [ -] H Representing the conjugate transpose operation of the matrix, N being the number of sampling points that meet the nyquist criterion, M being the oversampling factor,
representing a complex matrix of nm×1 (similar to the following).
In particular, for a common chirped (Linear Frequency Modulation, LFM) radar, the radar signal oversamples the data s n Can be expressed as:
s2, performing cyclic shift on the radar signal vector r obtained in the S1 to construct a Toeplitz matrix S:
s3, performing singular value decomposition on the Toeplitz matrix S obtained in the step S2 to analyze the characteristics of radar signals:
S＝UΔV H ＝U[Λ O]V H , (4)
wherein the method comprises the steps of
And->
For unitary matrix>
Sub-matrix Λ=diag (σ) 1 ,σ 2 ,…,σ NM ) NM singular values sigma for the Toeplitz matrix S 1 ,σ 2 ,…,σ NM A diagonal matrix of components, sigma 1 ≥σ 2 ≥…≥σ NM And (5) the matrix is equal to or larger than 0,O. />
S4, dividing U and Λ into a Dominant (Dominant, D) subspace (hereinafter referred to as a main space) and a Non-Dominant (Non-Dominant, ND) subspace (hereinafter referred to as a Non-main space) according to the singular value, setting L as the main space size (0 < L < NM), and simultaneously dividing V into blocks:
wherein the method comprises the steps of
Is a main space feature vector matrix, consists of L main space feature vectors,
is a matrix of non-principal space eigenvectors, and is composed of NM-L non-principal space eigenvectors, Λ D ＝diag(σ 1 ,σ 2 ,…,σ L ) Sum lambda ND ＝diag(σ L+1 ,σ L+2 ,…,σ NM ) The method comprises the steps of respectively representing a main space singular value matrix and a non-main space singular value matrix. V (V) a ,V b ,V c Sub-matrices of V, respectively,>
s5, reassigning the main space singular value and the non-main space singular value of the matrix delta in S4, namely reassigning the submatrix lambda of the matrix delta D Sum sub-matrix lambda ND Performing transformation, and setting the matrix after delta transformation as delta SVD Then constructing a waveform generation matrix:
P SVD ＝UΔ SVD V H , (6)
wherein delta is SVD ,
S6 randomly generating K column vectors d k As a waveform construction key,
k represents the number of waveforms in the communication waveform set.
P for S7 SVD And d k Multiplication to obtain K REC waveforms c SVD,k ：
c SVD,k ＝P SVD d k ,k＝1,2,…,K。 (7)
Further, for higher security of the REC system, the waveform construction key d is periodically replaced k 。
The singular value decomposition-based waveform design algorithm presented herein may measure the degree of similarity between the communication waveform and the radar echo, as compared to the eigenvalue decomposition-based conventional waveform design algorithm. Since the radar echo and REC waveforms are S and P respectively SVD Linear transformation of random vectors, i.e. UDeltaV H And U delta SVD V H Linear transformation of random vectors, therefore, can be performed by calculating uΔv H And U delta SVD V H Similarity between REC waveforms and radar echoes is measured by similarity between REC waveforms and radar echoes, here through the F rangeThe Euclidean distance between matrixes is calculated by number to measure similarity, and the similarity is expressed by parameter X:
wherein I II F Representing the F-norm of the matrix. The smaller the value of X, the higher the similarity between the REC waveform and the radar echo, the better the LPI performance, but the interference of the radar signal to the REC signal increases and the communication reliability decreases when the cooperative receiver makes a correlation decision.
The beneficial effects of the invention are as follows: (1) the similarity between the waveform designed by the radar embedded communication waveform design method based on singular value decomposition and the radar echo can be quantitatively calculated. (2) Compared with the traditional REC design method, the REC waveform design method provided by the invention can improve the freedom degree of waveform design by one time. (3) The REC waveform design method provided by the invention can greatly reduce the calculation complexity of a waveform design algorithm. (4) Compared with the traditional REC waveform design method, the REC waveform design method provided by the invention can not reduce the communication reliability and LPI performance.
Drawings
FIG. 1 is a schematic diagram of the operation of radar embedded communication;
FIG. 2 is a flow chart of a method of designing radar embedded communication waveforms based on singular value decomposition;
FIG. 3 is a flow chart of SVD-DP waveforms designed using the teachings of the present invention;
fig. 4 is a flowchart of an SVD-SDP waveform designed using the teachings of the present invention;
FIG. 5 is a graph of error rate for DP, SDP, SVD-DP, SVD-SDP waveforms;
fig. 6 is a normalized correlation coefficient curve of DP, SDP, SVD-DP, SVD-SDP waveforms.
Fig. 7 is a graph of the computational complexity of the DP, SDP, SVD-DP, SVD-SDP waveform design algorithm.
Detailed Description
The invention is further described below with reference to the drawings and the detailed description.
Fig. 2 is a flowchart of a method for designing radar embedded communication waveforms based on singular value decomposition, which can be divided into the following steps:
s1, after a radar irradiates an REC working area, an RF tag oversamples radar signals;
s2, circularly shifting an oversampled radar signal to construct a Toeplitz matrix;
s3, singular value decomposition is carried out on the Toeplitz matrix, and characteristics of radar signals are analyzed;
s4, dividing the radar signal into a main space component and a non-main space component according to the singular value size;
s5, constructing a waveform generation matrix based on singular value decomposition;
s6, randomly generating K waveform construction keys;
and S7, multiplying the waveform generation matrix by the K waveform construction keys to generate K REC waveforms, and periodically replacing the waveform construction keys to ensure the safety of the REC system.
The following design method based on singular value decomposition gives two specific cases
Case 1: SVD-DP waveform
FIG. 3 is a flowchart of SVD-DP waveforms designed by the technical scheme of the invention, and the specific steps are as follows:
s1, after a radar irradiates an REC working area, an RF tag oversamples radar signals;
s2, circularly shifting an oversampled radar signal to construct a Toeplitz matrix;
s3, singular value decomposition is carried out on the Toeplitz matrix, and characteristics of radar signals are analyzed;
s4, dividing the radar signal into a main space component and a non-main space component according to the singular value size;
s5, assigning zero to all singular values in the main space and assigning 1 to all singular values in the non-main space to generate a waveform generation matrix of the SVD-DP waveform
Wherein the method comprises the steps of
I NM-L Is NM-L order unit array.
S6 randomly generating K column vectors d k 
The key is constructed as a waveform.
P for S7 SVD-DP And d k The multiplication results in K SVD-DP waveforms:
case 2: SVD-SDP waveform
Fig. 4 is a flowchart of an SVD-SDP waveform designed by the technical scheme of the present invention, and the specific steps are as follows:
s1, after a radar irradiates an REC working area, an RF tag oversamples radar signals;
s2, circularly shifting an oversampled radar signal to construct a Toeplitz matrix;
s3, singular value decomposition is carried out on the Toeplitz matrix, and characteristics of radar signals are analyzed;
s4, dividing the radar signal into a main space component and a non-main space component according to the singular value size;
s5, all singular values in the main space are assigned with 0, singular values in the non-main space are unchanged, and a waveform generation matrix of SVD-SDP waveforms is generated
Wherein the method comprises the steps of
S6 randomly generating K column vectors d k 
The key is constructed as a waveform.
P for S7 SVD-SDP And d k Multiplying to obtain the kth SVD-SDP waveform
The invention is based on the following principle:
the REC waveform can be subjected to performance index evaluation from five aspects of communication reliability performance, LPI performance, REC waveform and radar echo similarity, waveform design freedom degree and waveform design algorithm complexity, and the evaluation indexes are as follows:
(1) Reliability performance index:
in REC systems, cooperative receivers need to suppress interference as much as possible to enhance the useful communication signal, where decorrelation filtering (decorrelating filter, DF) receivers (S.D.Blunt, P.Yatham and j. Stilles, "Intrapulse radar-embedded communications," IEEE Transactions on Aerospace Electronic Systems, vol.46, no.3, pp.1185-1200, jul.2010.) with excellent reception performance are employed. The DF receiver first generates K filter functions:
wherein the method comprises the steps of
The DF receiver carries out correlation calculation on the received signal and K filter functions one by one, and then judges the waveform with highest correlation as the received waveform. The judging method comprises the following steps:
Signal-to-Noise Ratio (SCR) is defined as the REC Signal power to radar echo power Ratio, and Signal-to-Noise Ratio (SNR) is defined as the REC Signal power to ambient Noise power Ratio. The SCR is fixed, the SNR is changed, and the symbol error rate (Symbol Error Rate, SER) of the DF receiver under different SNR conditions can be obtained, so that the communication reliability of the designed communication waveform can be measured.
(2) LPI performance index:
since the concealment of the REC is achieved by hiding the communication waveform in the high-power radar wave, the conventional method for measuring the anti-interception performance, such as by measuring the intercepted signal energy, is not applicable to the REC case.
Assuming that the design principle of the REC, LFM signal parameters, time-width bandwidth product and oversampling factor are known to the interception receiver, the interception receiver can construct a topril matrix S and perform eigenvalue decomposition, then perform non-main space projection on a received vector by predicting the main space size to obtain non-main space waveform information, and herein, evaluate LPI performance by performing normalization correlation processing on an estimated waveform obtained after projection by the interception receiver and an original REC waveform.
Assume that the acquisition receiver estimates the primary space size as
Predicting the main space matrix as +.>
It is composed of->
The feature vector corresponding to the maximum feature value is composed, and the prediction projection matrix can be expressed as:
wherein the method comprises the steps of
I NM For NM order unit matrix,/->
To predict non-primary spatial matrices. Use->
Performing projection processing on the intercepted signals to obtain estimated waveforms:
where r is the signal to be intercepted,
to intercept the estimated waveform obtained after the projection of the receiver. Finally calculate->
With the actual communication waveform c k Normalized correlation coefficient +.>
Wherein the method comprises the steps of
Although the normalized correlation coefficient cannot directly represent the interception probability, the normalized correlation coefficient can effectively measure the accuracy of the interception receiver to extract the interception waveform, and provides an effective reference for the LPI performance. />
The larger the value, the higher the accuracy of estimating the REC waveform, i.e., the worse the LPI performance, is represented by the intercept receiver.
(3) REC waveform and radar echo similarity index
a) Similarity calculation of SVD-DP waveform and radar echo
Due to the radar echo and SVD-DP waveforms, respectivelyIs S and
linear transformation of random vectors, i.e. UDeltaV H And U delta SVD-DP V H Linear transformation of random vectors, therefore, can be performed by calculating uΔv H And U delta SVD-DP V H The similarity between two waveforms and radar echo is measured to obtain the similarity degree X of two waveforms and radar echo 1 X is obtainable from formula (8) 1 The method comprises the following steps:
from X 1 The similarity of the SVD-DP waveform to the radar echo is related to the singular values of both the dominant and non-dominant spaces. The similarity of the SVD-DP waveform to the radar echo can be changed by adjusting the main space size.
b) Similarity calculation of SVD-SDP waveform and radar echo
Since the radar echo and SVD-SDP waveforms are S and S, respectively
Linear transformation of random vectors, i.e. UDeltaV H And U delta SVD-SDP V H Linear transformation of random vectors, therefore, can be performed by calculating uΔv H And U delta SVD-SDP V H The similarity between two waveforms and radar echo is measured to obtain the similarity degree X of two waveforms and radar echo 2 X is obtainable from formula (8) 2 The method comprises the following steps:
wherein V is bc ＝[V b V c ]. From X 2 The similarity of the SVD-SDP waveform to the radar echo is only related to the dominant spatial singular values and is inversely related to the sum of the squares of the dominant spatial singular values. The phase of the SVD-SDP waveform and the radar echo can thus be adjusted by changing the main space sizeSimilarity.
(4) Waveform design freedom index:
an excellent REC waveform design algorithm should be able to generate enough REC waveforms to periodically alter the REC waveform set, reducing the probability of being monitored and even intercepted over time, thereby enhancing the safety and concealment of the REC system. In order to quantitatively compare the number of waveforms that can be generated by each waveform design algorithm, a concept of design freedom is defined. With reference to the statistical definition, the design freedom is defined as follows: the REC waveform algorithm design freedom value is equal to the number of independent or free variables in the REC waveform construction process. The higher the degree of freedom of design, the better the algorithm, the more the degree of freedom of design of the REC waveform algorithm is denoted by G below.
For the DP waveform design algorithm, the DP waveform design algorithm is obtained by multiplying a key vector by a principal and subordinate space projection matrix, and the key vector comprises NM independent free variables, so that the design freedom degree of the DP algorithm is
G DP ＝NM. (20)
For SDP waveform design algorithm, the algorithm is similar to the DP algorithm, except that the projection matrix of SDP waveform uses non-main space eigenvalue matrix, its key vector contains NM independent free variables, so the design freedom of SDP algorithm is
G SDP ＝NM. (21)
For SVD-DP waveform, its key vector d is known from case 1 algorithm step S7 k Contains 2NM-1 independent free variables, so the SVD-DP algorithm has the design freedom degree of
G SVD-DP ＝2NM-1. (22)
For SVD-SDP waveform, its key vector d is known from case 2 algorithm step S7 k Contains 2NM-1 independent free variables, so the SVD-SDP algorithm has the design freedom degree of
G SVD-SDP ＝2NM-1. (23)
To visually compare the degree of freedom in designing the four REC waveform algorithms described above, equations (20) - (23) are summarized in the following table. In general, NM > 1, namely (2 NM-1)/NM approximately equal to 2, namely, the REC waveform design method based on singular value decomposition can improve the freedom degree of waveform design by approximately one time.
| REC waveform | Degree of freedom of design |
| DP | NM |
| SDP | NM |
| SVD-DP | 2NM–1 |
| SVD-SDP | 2NM–1 |
(5) Calculating complexity indexes by a waveform design algorithm:
the computational complexity of the REC waveform design algorithm affects the response delay of the RF tag, the time accuracy of the embedded REC signal, and the concealment.
For the DP algorithm, the matrix S is converted into a square matrix S H S, performing K times of eigenvalue decomposition. Then, K projection matrices are generated and multiplied by the key vector K times. Therefore, the computational complexity of the DP algorithm is
Compared with the DP algorithm, the projection matrix of the SDP waveform design algorithm uses the eigenvalue matrix, and the computation complexity of the SDP algorithm is as follows
For the SVD-DP algorithm, the matrix S is subjected to 1-degree eigenvalue decomposition. Then, 1 projection matrix P is generated SVD-DP And with key vector d k Multiplying K times. Therefore, the SVD-DP algorithm has a computational complexity of
Compared with SVD-DP algorithm, the projection matrix of SVD-SDP waveform design algorithm uses eigenvalue matrix, and the calculation complexity of SVD-SDP algorithm is
Typically NM > L > K, the four REC waveform algorithms described above have a computational complexity of about
Obtainable by formulae (24) and (25)
T SDP -T DP ＝O(K(NM)(NM-L) 2 )＞0. (29)
Obtainable by formulae (26) and (27)
T SVD-SDP -T SVD-DP ＝O((NM)(NM-L) 2 )＞0. (30)
Assume that
Then 0 < a < 1. Obtainable from (60)
Let f (K) = (2-a) K-a 2 +4a-5, typically the number of communication symbols, K.gtoreq.3, therefore
f(K)≥f(3)＝-a 2 +a+1＝a(1-a)+1＞0. (32)
Therefore, the formula (31) can be rewritten as
T DP -T SVD-SDP ＝O(f(K)(NM) 3 )＞0. (33)
The magnitude relation of the calculation complexity of the four algorithms can be obtained by the formulas (29), (30) and (33)
T SDP ＞T DP ＞T SVD-SDP ＞T SVD-DP . (34)
This shows that the computational complexity of SVD-DP and SVD-SDP algorithms designed based on the waveform design method proposed by the present invention is lower than that of conventional DP and SDP algorithms.
Fig. 5 is a graph of symbol error rate of SVD-DP waveform and SVD-SDP waveform constructed by the method of the present invention and conventional DP and SDP waveforms at different SNRs, where the cooperative receiver employs a DF receiver, the radar signal selects LFM signal, assuming that the radar and noise follow gaussian distribution, SCR is set to-24 dB, and other parameters are set as: n=100, m=2, l=100, k=4. It can be seen that the symbol error rates of the DP waveform and the SVD-DP waveform are close, i.e., the communication reliability performance of both are close. When snr=6 dB, the SVD-SDP waveform can reduce the symbol error rate from 2×10 compared to the SDP waveform -3 Down to 6X 10 -4 I.e. the communication reliability performance of the SVD-SDP waveform is superior to the SDP waveform. Therefore, compared with the traditional REC waveform, the REC waveform designed based on the waveform design method provided by the invention has the advantage that the communication reliability is not deteriorated.
Fig. 6 further simulates normalized correlation coefficients for DP, SDP, SVD-DP and SVD-SDP waveforms, SCR was set to-24 dB, snr was set to-10 dB, and other parameters were consistent with fig. 5. It can be seen that the normalized correlation coefficients of the DP waveform and the SVD-DP waveform are similar, i.e., the LPI performance of both are similar. The normalized correlation coefficient of the SDP waveform and the SVD-SDP waveform is similar, i.e. the LPI performance of the SDP waveform and the SVD-SDP waveform is similar. Therefore, compared with the traditional REC waveform, the REC waveform designed based on the waveform design method provided by the invention has the advantage that the LPI performance is not attenuated.
Fig. 7 shows the computational complexity of the four waveform design algorithms DP, SDP, SVD-DP and SVD-SDP at different main space sizes, where the number of communication symbols K is set to k=4 (2 bits) or k=8 (3 bits). As can be seen, the magnitude relation of the four REC waveform design algorithms is consistent with equation (34), and the computational complexity of the four REC waveform design algorithms decreases as the main space size increases. If the main space ratio is set to 50% and the number of communication waveforms is set to k=4 (k=8), the computational complexity of the SVD-DP and SVD-SDP algorithms is reduced by 37.5% (64.3%) and 41.7% (67.2%) compared to the conventional DP and SDP algorithms, respectively. These results show that compared with the traditional DP and SDP algorithms, the REC waveform design method based on singular value decomposition can reduce the calculation complexity of the algorithms, shorten the time required for generating the REC waveform, reduce the response delay and enhance the concealment of the REC system.
In summary, compared with the traditional REC waveform, the similarity between the REC waveform constructed by the REC waveform design method based on singular value decomposition and the radar echo can be quantized, the freedom degree of waveform design is doubled on the premise of not reducing the communication reliability and anti-interception performance of the REC waveform, and meanwhile, the complexity of a waveform design algorithm is greatly reduced.
Claims (5)
1. A radar embedded communication waveform design method based on singular value decomposition is characterized by comprising the following steps:
after the S1 REC working area is irradiated by the radar, the radio frequency tag oversamples radar signals, and a radar signal vector r with a sampling length of NM is expressed as:
r＝[s 1 ,s 2 ,s 3 ,…,s NM ] H , (1)
where r is the sampled radar signal vector, s 1 ,s 2 ,s 3 ,…,s NM Oversampling data for radar signals, [ -] H Representing the conjugate transpose operation of the matrix, N being the number of sampling points that meet the nyquist criterion, M being the oversampling factor,
representing a complex matrix of NM x 1;
s2, performing cyclic shift on the radar signal vector r obtained in the S1 to construct a Toeplitz matrix S:
s3, performing singular value decomposition on the Toeplitz matrix S obtained in the step S2 to analyze the characteristics of radar signals:
S＝UΔV H ＝U[Λ O]V H , (4)
wherein the method comprises the steps of
And->
For unitary matrix>
Sub-matrix Λ=diag (σ) 1 ,σ 2 ,…,σ NM ) NM singular values sigma for the Toeplitz matrix S 1 ,σ 2 ,…,σ NM A diagonal matrix of components, sigma 1 ≥σ 2 ≥…≥σ NM The matrix is equal to or more than 0,O;
s4, dividing U and Λ into a main space and a non-main space according to the singular value, setting L as the main space, setting 0 < L < NM, and simultaneously partitioning V into blocks:
wherein the method comprises the steps of
Is a main space feature vector matrix, which consists of L main space feature vectors, and is +.>
Is a matrix of non-principal space eigenvectors, composed of NM-L non-principal space eigenvectors，Λ D ＝diag(σ 1 ,σ 2 ,…,σ L ) Sum lambda ND ＝diag(σ L+1 ,σ L+2 ,…,σ NM ) V is the main space singular value matrix and the non-main space singular value matrix respectively a ,V b ,V c Sub-matrices of V, respectively,>
s5, reassigning the main space singular value and the non-main space singular value of the matrix delta in S4: assigning zero to all singular values in the main space and assigning 1 to all singular values in the non-main space to generate a waveform generation matrix of the SVD-DP waveform:
wherein the method comprises the steps of
Ι NM-L Is NM-L order unit array;
s6 randomly generating K column vectors d k As a waveform construction key,
k represents the number of waveforms in the communication waveform set;
p for S7 SVD-DP And d k The multiplication results in K SVD-DP waveforms:
2. a method of designing a radar embedded communication waveform based on singular value decomposition according to claim 1, wherein: in S1, for a common chirp radar, the radar signal oversamples data S n Expressed as:
3. a method of designing a radar embedded communication waveform based on singular value decomposition according to claim 1, wherein: in S5, the following reassignment is carried out on the main space singular value and the non-main space singular value of the matrix delta in S4: all singular values of the main space are assigned with 0, singular values of the non-main space are unchanged, and a waveform generation matrix of SVD-SDP waveforms is generated
Wherein the method comprises the steps of
。
4. A method of designing a radar embedded communication waveform based on singular value decomposition according to claim 3, wherein: s7, use P SVD-SDP And d k Multiplying to obtain the kth SVD-SDP waveform
5. A radar embedded communication waveform design method based on singular value decomposition according to any one of claims 1 to 4, characterized in that: for higher security of REC system, the waveform construction key d is replaced periodically k 。
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